# A triangle has sides with lengths: 2, 9, 2. How do you find the area of the triangle using Heron's formula?

##### 1 Answer

There is no such triangle, since

#### Explanation:

If a triangle has sides of length

#a+b > c#

#b+c > a#

#c+a > b#

...unless you count empty triangles, in which case change the

If you try to apply Heron's formula to lengths

The semi-perimeter

#sp = (a+b+c)/2 = (2+9+2)/2 = 13/2#

Then Heron's formula for the area

#A = sqrt(sp(sp-a)(sp-b)(sp-c))#

#=sqrt(13/2(13/2-2)(13/2-9)(13/2-2))#

#=sqrt((13/2)(9/2)(-5/2)(9/2))#

#=sqrt(-5265/16)#

It is possible to simplify this further, but there's no real point since it's clearly the square root of a negative quantity.